Kline 1972, pp. 807–808 Augustin Cauchy (1839) "Mémoire sur l'intégration des équations linéaires" (Memoir on the integration of linear equations), Comptes rendus, 8: 827–830, 845–865, 889–907, 931–937. From p. 827:"On sait d'ailleurs qu'en suivant la méthode de Lagrange, on obtient pour valeur générale de la variable prinicipale une fonction dans laquelle entrent avec la variable principale les racines d'une certaine équation que j'appellerai l'équation caractéristique, le degré de cette équation étant précisément l'order de l'équation différentielle qu'il s'agit d'intégrer." (One knows, moreover, that by following Lagrange's method, one obtains for the general value of the principal variable a function in which there appear, together with the principal variable, the roots of a certain equation that I will call the "characteristic equation", the degree of this equation being precisely the order of the differential equation that must be integrated.) Kline, Morris (1972), Mathematical thought from ancient to modern times, Oxford University Press, ISBN0-19-501496-0
David Hilbert (1904) "Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. (Erste Mitteilung)" (Fundamentals of a general theory of linear integral equations. (First report)), Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse (News of the Philosophical Society at Göttingen, mathematical-physical section), pp. 49–91. From p. 51:"Insbesondere in dieser ersten Mitteilung gelange ich zu Formeln, die die Entwickelung einer willkürlichen Funktion nach gewissen ausgezeichneten Funktionen, die ich 'Eigenfunktionen' nenne, liefern: …" (In particular, in this first report I arrive at formulas that provide the [series] development of an arbitrary function in terms of some distinctive functions, which I call eigenfunctions: … ) Later on the same page: "Dieser Erfolg ist wesentlich durch den Umstand bedingt, daß ich nicht, wie es bisher geschah, in erster Linie auf den Beweis für die Existenz der Eigenwerte ausgehe, … "
Korn & Korn 2000, Section 14.3.5a. Korn, Granino A.; Korn, Theresa M. (2000), “Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review”, New York: McGraw-Hill (ấn bản thứ 2), Bibcode:1968mhse.book.....K, ISBN0-486-41147-8
loc.gov
lccn.loc.gov
Nering 1970, tr. 38. Nering, Evar D. (1970), Linear Algebra and Matrix Theory (ấn bản thứ 2), New York: Wiley, LCCN76091646
For a proof of this lemma, see Roman 2008, Theorem 8.2 on p. 186; Shilov 1977, p. 109; Hefferon 2001, p. 364; Beezer 2006, Theorem EDELI on p. 469; and Lemma for linear independence of eigenvectors Roman, Steven (2008), Advanced linear algebra (ấn bản thứ 3), New York: Springer Science + Business Media, ISBN978-0-387-72828-5 Shilov, Georgi E. (1977), Linear algebra, Translated and edited by Richard A. Silverman, New York: Dover Publications, ISBN0-486-63518-X Hefferon, Jim (2001), Linear Algebra, Colchester, VT: Online book, St Michael's College, Bản gốc lưu trữ ngày 1 tháng 3 năm 2014, truy cập ngày 1 tháng 3 năm 2021 Beezer, Robert A. (2006), A first course in linear algebra, Free online book under GNU licence, University of Puget Sound
For a proof of this lemma, see Roman 2008, Theorem 8.2 on p. 186; Shilov 1977, p. 109; Hefferon 2001, p. 364; Beezer 2006, Theorem EDELI on p. 469; and Lemma for linear independence of eigenvectors Roman, Steven (2008), Advanced linear algebra (ấn bản thứ 3), New York: Springer Science + Business Media, ISBN978-0-387-72828-5 Shilov, Georgi E. (1977), Linear algebra, Translated and edited by Richard A. Silverman, New York: Dover Publications, ISBN0-486-63518-X Hefferon, Jim (2001), Linear Algebra, Colchester, VT: Online book, St Michael's College, Bản gốc lưu trữ ngày 1 tháng 3 năm 2014, truy cập ngày 1 tháng 3 năm 2021 Beezer, Robert A. (2006), A first course in linear algebra, Free online book under GNU licence, University of Puget Sound
web.archive.org
For a proof of this lemma, see Roman 2008, Theorem 8.2 on p. 186; Shilov 1977, p. 109; Hefferon 2001, p. 364; Beezer 2006, Theorem EDELI on p. 469; and Lemma for linear independence of eigenvectors Roman, Steven (2008), Advanced linear algebra (ấn bản thứ 3), New York: Springer Science + Business Media, ISBN978-0-387-72828-5 Shilov, Georgi E. (1977), Linear algebra, Translated and edited by Richard A. Silverman, New York: Dover Publications, ISBN0-486-63518-X Hefferon, Jim (2001), Linear Algebra, Colchester, VT: Online book, St Michael's College, Bản gốc lưu trữ ngày 1 tháng 3 năm 2014, truy cập ngày 1 tháng 3 năm 2021 Beezer, Robert A. (2006), A first course in linear algebra, Free online book under GNU licence, University of Puget Sound
For a proof of this lemma, see Roman 2008, Theorem 8.2 on p. 186; Shilov 1977, p. 109; Hefferon 2001, p. 364; Beezer 2006, Theorem EDELI on p. 469; and Lemma for linear independence of eigenvectors Roman, Steven (2008), Advanced linear algebra (ấn bản thứ 3), New York: Springer Science + Business Media, ISBN978-0-387-72828-5 Shilov, Georgi E. (1977), Linear algebra, Translated and edited by Richard A. Silverman, New York: Dover Publications, ISBN0-486-63518-X Hefferon, Jim (2001), Linear Algebra, Colchester, VT: Online book, St Michael's College, Bản gốc lưu trữ ngày 1 tháng 3 năm 2014, truy cập ngày 1 tháng 3 năm 2021 Beezer, Robert A. (2006), A first course in linear algebra, Free online book under GNU licence, University of Puget Sound
